15 September 2011, Volume 54 Issue 5

    

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  Weighted Boundedness for Commutators of One-Sided Operators

  Zun Wei FU, Yan LIN

  Acta Mathematica Sinica, Chinese Series. 2011, 54(5): 705-714. https://doi.org/10.12386/A2011sxxb0074

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  Using extrapolation of one-sided weights, the authors establish one-sided weighted strong type inequalities for commutators generated by one-sided operators and Lipschitz functions. Moreover, a sufficient and necessary condition for the corresponding boundedness of commutators of two kinds of one-sided maximal operators will be given.  
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  Characterization of Generators for Multiresolution

  Nian Ying MAO, Xian Liang SHI

  Acta Mathematica Sinica, Chinese Series. 2011, 54(5): 715-720. https://doi.org/10.12386/A2011sxxb0075

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  A characterization on Gibbs phenomenon for convolution operators at a simple discontinuity of a function is established. Furthermore, some examples are given.  
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  The Boundedness of the Hardy–Littlewood Maximal Function on the Weighted Orlicz–Morrey Spaces

  Yong ZHONG, Hou Yu JIA

  Acta Mathematica Sinica, Chinese Series. 2011, 54(5): 721-730. https://doi.org/10.12386/A2011sxxb0076

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  We obtain the boundedness of the maximal operator M_ω(|f|^p)^(1/p)and M(f) on the weighted Orlicz–Morrey spaces. On the other hand, we get a necessary condition for the boundedness of the maximal operator M_ω(|f|^p)^(1/p).  
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  The Construction of Symmetric or Antisymmetric Multiwavelets with Composite Dilations

  Guo Chang WU, Xin Xian TIAN, Deng Feng LI

  Acta Mathematica Sinica, Chinese Series. 2011, 54(5): 731-738. https://doi.org/10.12386/A2011sxxb0077

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  Based on existing wavelets with composite dilations, we give a way of constructing symmetric or antisymmetric multiwavelets with composite dilations. This way can increase the amount of wavelets with composite dilations. Furthermore, new multiwavelets preserve the most properties of old wavelets.  
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  The Central Extension of Inner Abelian p-Groups (IV)

  Hai Peng QU, Li Feng ZHENG

  Acta Mathematica Sinica, Chinese Series. 2011, 54(5): 739-752. https://doi.org/10.12386/A2011sxxb0078

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  Assume N and H are groups. If there is a group G which has a normal subgroup Ñ ≤ Z(G) such that Ñ ≌ N and G/Ñ ≌ H, then G is called a central extension of N by H. In this paper, we classified all groups which are central extensions of N by H, where N is an elementary abelian p-group of order p³ and H is an inner abelian p-group. Thus all groups which are central extensions of an elementary abelian p-group by an inner abelian p-group are classified.  
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  2-Cohomology Group on the Generalized Weyl Type Lie Algebras W × gl_n(F)

  Guang Ai SONG, Zhong Jie LI, Mei Yan WANG

  Acta Mathematica Sinica, Chinese Series. 2011, 54(5): 753-766. https://doi.org/10.12386/A2011sxxb0079

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  Let F be a field with characteristic zero, let W be a generalized Weyl type algebra over F, and gl_n(F) the general linear algebra, then there is induced Lie algebra structure on the associative algebra W gl_n(F). In the present paper, we consider the 2-cohomology group structures of the Lie algebra W gl_n(F).  
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  The Characterizations of A-Parseval Frame Wavelet

  Yong Dong HUANG, Na SUN

  Acta Mathematica Sinica, Chinese Series. 2011, 54(5): 767-790. https://doi.org/10.12386/A2011sxxb0080

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  In this paper, the characterization of Parseval frame wavelets with dilation matrix A (A-PFW)is studied, where A satisfies A³ = 2I₃ and the sums of the elements in each column are even number.Firstly,the relation of Parseval frame wavelets with special dilation matrix B (B-PFW) and Parseval frame wavelets with special dilation matrix C (C-PFW) is discussed, and at the same time the equivalence relations of C-PFW) and Parseval frame wavelets with two kinds of special dilation matrices D, (D-PFW, -PFW) are gave. Secondly, the characterizations of pseudo-scaling function and MRA Parseval frame wavelets with dilation matrix A (MRA A-PFW) are presented.Finally,by means of dimensional function, a sufficient and necessary condition for an A-PFW to be an MRA A-PFW is obtained.  
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  Nonlinear Lie Derivations on Factor von Neumann Algebras

  Fang Juan ZHANG, Jian Hua ZHANG, Lin CHEN, Xin Hong ZHU

  Acta Mathematica Sinica, Chinese Series. 2011, 54(5): 791-802. https://doi.org/10.12386/A2011sxxb0081

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  Let M be a factor von Neumann algebra acting on a complex separable Hilbert space H with dim H > 2. We prove that every nonlinear Lie derivation on a factor von Neumann algebra M is of the form A → φ(A)+h(A)I, where φ : M → M is an additive derivation and h : M → C is a nonlinear map with h(AB-BA) = 0 for all A,B ∈ M.  
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  A Fan-Fype Condition for the Existence of [a, b]-Factors

  Si Zhong ZHOU

  Acta Mathematica Sinica, Chinese Series. 2011, 54(5): 803-810. https://doi.org/10.12386/A2011sxxb0082

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  Let G be a graph, and let a, b be two integers with 0 ≤ a ≤ b. Then a spanning subgraph F of G is called an [a, b]-factor if a ≤ d_F (x) ≤ b holds for each x ∈ V (G). In this paper, we obtain a Fan-type condition for the existence of [a, b]- factors with prescribed properties. Furthermore, it is shown that the result in this paper is sharp.  
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  On the Stability of Generalized f-Projection Operators with an Application

  Xi LI Nan, Jing HUANG, Yun Zhi ZOU

  Acta Mathematica Sinica, Chinese Series. 2011, 54(5): 811-822. https://doi.org/10.12386/A2011sxxb0083

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  In this paper, the stability of generalized f-projection operators with a perturbation of the set is studied in Banach spaces. As an application, a perturbed iterative algorithm involving the generalized f-projection operator for solving a class of generalized variational inequality problem in Banach spaces is constructed.  
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  Numerical Solutions of Jump Diffusions with Markovian Switching

  Jun YE, Kai LI

  Acta Mathematica Sinica, Chinese Series. 2011, 54(5): 823-838. https://doi.org/10.12386/A2011sxxb0084

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  We consider the numerical solutions for a class of jump diffusions with Markovian switching. After briefly reviewing necessary notions, a new jump-adapted efficient algorithm based on the Euler scheme is constructed for approximating the exact solution. Under some general conditions, it is proved that the numerical solution through such scheme converge to the exact solution. Moreover, the order of the error between the numerical solution and the exact solution is also derived. Numerical experiments are carried out to show the computational efficiency of the approximation.  
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  Reflected Backward Stochastic Differential Equation Driven by Lévy Processes

  Xi Liang FAN, Yong REN

  Acta Mathematica Sinica, Chinese Series. 2011, 54(5): 839-852. https://doi.org/10.12386/A2011sxxb0085

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  We prove the existence, uniqueness and stability of the solutions for reflected backward stochastic differential equation driven by Lévy processes with locally Lipschitz coefficients. Furthermore, we prove the regularity of the process K in the case when the barrier is regular and the coefficient is Lipschitz.  
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  A Stochastic Modified Lotka–Volterra Competition Model

  Jing Liang Lü, Ke WANG

  Acta Mathematica Sinica, Chinese Series. 2011, 54(5): 853-860. https://doi.org/10.12386/A2011sxxb0086

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  This paper discusses stochastic two-species modified Lotka–Volterra competition model. Both white and color environmental noises will be taken into account. The sufficient conditions for some population dynamical properties including the existence of global positive solutions, stochastic ultimate boundedness, stochastic permanence, stochastic extinction will be obtained.  
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  The Isolated Scattering Number of Graphs

  Shi Ying WANG, Yu Xing YANG, Shang Wei LIN, Jing LI, Zhi Ming HU

  Acta Mathematica Sinica, Chinese Series. 2011, 54(5): 861-874. https://doi.org/10.12386/A2011sxxb0087

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  The isolated scattering number isc(G) = max{i(G - S) - |S| : S ∈ C(G)}, where G is a connected graph, i(G - S) is the number of isolated vertices of G - S and C(G) is the set of vertex cuts of G. In this paper, we investigate the relationships between the isolated scattering number and other parameters of a graph G, and discuss the graphs with special isolated scattering numbers. We prove that the isolated scattering numbers of a cycle, a connected bipartite graph, the join of connected bipartite graphs and the complement of a tree and a cycle are minimal, and give the maximum and minimum isolated scattering numbers of trees with given order and maximum degree.  
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  Directional Derivatives and Generalized Cone-Preinvex Set-Valued Optimization

  Guo Lin YU

  Acta Mathematica Sinica, Chinese Series. 2011, 54(5): 875-880. https://doi.org/10.12386/A2011sxxb0088

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  This note deals with the optimality conditions of set-valued unconstraint optimization problems in topological vector spaces. Based upon the concepts of Dini directional derivatives and generalized cone-preinvexity for the set-valued mappings, the necessary and sufficient optimality conditions are established for weak and strong minimizer respectively in set-valued optimization problems.